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On the lengths of certain chains of subalgebras in Lie algebras

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>2014
<mark>Journal</mark>Communications in Algebra
Issue number11
Volume42
Number of pages12
Pages (from-to)4778-4789
Publication statusPublished
Original languageEnglish

Abstract

In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal length in which each subalgebra is a quasi-ideal of L. In particular we show that, over a field F of characteristic zero, a Lie algebra L with radical R has a maximal chain of subalgebras and a chain of subalgebras all of which are modular in L of the same length if and only if L = R, or ??? and L/R is a direct sum of isomorphic three-dimensional simple Lie algebras.